Dr. rer. nat. Dipl.Math. Felix Govaers
Stellv. Abteilungsleiter Sensordaten und Informationsfusion

Research Interests
My research is focussed on the following topics:
 TracktoTrack Fusion for distributed multi sensor applications: Multiple sensors can provide better estimation performance because each additional sensor contributes more information. Centralized fusion of the measurements from all sensors at a single node is theoretically optimal because the information in the measurements is not degraded by any intermediate processing. However, centralized fusion is not always feasible when communication bandwidth is limited. Thus many systems use a distributed estimation or fusion architecture where the individual sensors process their measurements to generate local estimates and error covariances, which are then sent to a fusion node to be combined into global state estimates and estimation error covariances. For optimal processing, crosscorrelations of estimates of distributed fusion nodes have to be considered. The Distributed Kalman Filter (DKF) provides an optimal solution in the case of known measurement error covariances and linear measurment functions. Approximations in other cases can be obtained.
 OutofSequence Processing: In real–world application of sensor data fusion, one has to be aware of out–of–sequence (OoS) measurements. Due to latencies in the underlying communication infrastructure, for example, such measurements arrive at a processing node in a distributed data fusion system “too late”, i.e. after sensor data with a later time stamp already been processed. For optimal processing of OoS data, crosscorrelations of the measurement and the estimate have to be considered. We are working on solutions which are based on the Accumulated State Densities (ASDs). These provide a closed form solution to the joint density of a full trajectory and therefore yields the structure of statistical dependencies in time.
 Path Integral Formulation of the target tracking problem: There is a connection between target tracking and quantum physics which can be revealed by means of a path integral formulation. The theory of quantum physics tells us that the character of objects with respect to their position and kinematics is inherently of probabilistic nature. According to Heisenberg’s principle of uncertainty, the state of particles on a sub–atomic scale can only be described in terms of probabilities. The temporal evolution of these probabilities is given by the Schrödinger equation which is an analogon to the diffusion equation. This analogy already indicates a ‘principle of uncertainty’ on a macroscopic level, which nowadays is known as the laws of statistical mechanics. This research field considers for instance the temporal evolution of a particle distribution influenced by the random collisions with surrounding atoms or molecules. This yields a random motion which was at first examined with probabilistic means by Robert Brown and is therefore known as the Brownian motion. It turns out that the very same stochastic model is also highly useful when it comes to tracking objects at even larger scales.
 Parafac/Candecomp tensor decomposition for nonlinear state estimation: In target tracking applications, one often faces high dimensional state vectors as not only the Cartesian coordinates of the target are of interest, but also the velocity, heading, and other parameters belonging to nonlinear higherorder dynamic models when the target performs tactical manoeuvres. In many appplications nonlinear filtering is required in real time which is a demanding issue due to the ’curse of dimensionality’ which originates from the simple fact that even when the pdf is discretized, the number of grid points on equidistant grids grows exponentially.
The continuoustime evolution of the pdf is governed by a partial differential equation, the FokkerPlanck equation (FPE), and for its numerical solution there exist numerous methods. Well known are finite element methods and finite difference methods, but due to the curse of dimensionality, this only works up to a very limited dimensionality. The Parafac tensor decomposition represents a function (pdf) by means of an outer prodcut of discretized vectors. It has been noticed that a sum of such outer products has astonishing approximation features while the computational processing load and required memory only grows linear in the dimension. This allows to represent a pdf with much higher accuracy than Gaussian filters for instance would do.
Teaching
Winter 2020/2021
 Lecture "Sensor Data Fusion  Methods and Applications"
 Seminar "Sensor Data Fusion"
Winter 2019/2020
 Lecture "Sensor Data Fusion  Methods and Applications"
 Seminar "Sensor Data Fusion"
 Lecture "Advanced Sensor Data Fusion in Distributed Systems"
 Lecture "Einführung in die Sensordatenfusion"
 Lab "Sensor Data Fusion"
Winter 2018/2019
 Lecture "Sensor Data Fusion  Methods and Applications"
 Seminar "Sensor Data Fusion"
 Lecture "Advanced Sensor Data Fusion in Distributed Systems"
 Lecture "Einführung in die Sensordatenfusion"
 Lab "Sensor Data Fusion"
Winter 2017/2018
 Lecture "Sensor Data Fusion  Methods and Applications"
 Seminar "Sensor Data Fusion"
 Lecture "Advanced Sensor Data Fusion in Distributed Systems"
 Lecture "Einführung in die Sensordatenfusion"
 Lab "Sensor Data Fusion"
Winter 2016/2017
 Lecture "Sensor Data Fusion  Methods and Applications"
 Seminar "Sensor Data Fusion"
 Lecture "Advanced Sensor Data Fusion in Distributed Systems"
 Lecture "Einführung in die Sensordatenfusion"
 Lab "Sensor Data Fusion"
Winter 2016/2017
 Advisor for practical exercises of lecture "Sensor Data Fusion  Methods and Applications"
 Advisor for seminar "Sensor Data Fusion"
 Lecture "Advanced Sensor Data Fusion in Distributed Systems"
 Advisor for practical exercises in lecture "Einführung in die Sensordatenfusion"
 Advisor for lab "Sensor Data Fusion"
Winter 2015/2016
 Advisor for practical exercises of lecture "Sensor Data Fusion  Methods and Applications"
 Advisor for seminar "Sensor Data Fusion"
 Lecture "Advanced Sensor Data Fusion in Distributed Systems"
 Advisor for practical exercises in lecture "Einführung in die Sensordatenfusion"
 Advisor for lab "Sensor Data Fusion"
Winter 2014/2015
 Advisor for practical exercises of lecture "Sensor Data Fusion  Methods and Applications"
 Advisor for seminar "Sensor Data Fusion"
 Lecture "Advanced Sensor Data Fusion in Distributed Systems"
 Advisor for practical exercises in lecture "Einführung in die Sensordatenfusion"
 Advisor for lab "Sensor Data Fusion"
Winter 2013/2014
 Advisor for practical exercises of lecture "Sensor Data Fusion  Methods and Applications"
 Advisor for seminar "Sensor Data Fusion"
 Advisor for practical exercises in lecture "Einführung in die Sensordatenfusion"
 Advisor for lab "Sensor Data Fusion"
Winter 2012/2013
 Advisor for practical exercises of lecture "Sensor Data Fusion  Methods and Applications"
 Advisor for seminar "Sensor Data Fusion"
 Advisor for practical exercises in lecture "Einführung in die Sensordatenfusion"
 Advisor for lab "Sensor Data Fusion"
Winter 2011/2012
 Advisor for practical exercises of lecture "Sensor Data Fusion  Methods and Applications"
 Advisor for seminar "Sensor Data Fusion"
 Advisor for practical exercises in lecture "Einführung in die Sensordatenfusion"
 Advisor for lab "Sensor Data Fusion"